def main():
image = lena().astype(np.float) / 255.
h, w = image.shape
y_true = image.ravel()
noise = np.random.normal(0, 0.1, y_true.shape)
y_noisy = y_true + noise
grad = image_gradient_operator(h, w)
l1 = 0.1 * GroupL1Norm((2, h, w), 0)
#l1 = 0.1 * SliceSeparableNorm(L2Norm(), (2, h * w), 1)
l2 = L2Distance(y_noisy)
obj = lambda x: l1(grad * x) + l2(x)
algo = APGM(l2,
l1,
A=grad,
maxiter=50,
x0=y_noisy,
objectives=ObjectiveLogger(obj),
errors=ErrorLogger(y_true))
t0 = time.time()
y_denoised = algo.run()
print "took %.3f seconds" % (time.time() - t0)
pl.figure()
pl.gray()
for i, (title, v) in enumerate([('ground truth', y_true),
('noisy', y_noisy),
('denoised', y_denoised)]):
pl.subplot(2, 3, i + 1)
pl.title(title)
pl.xticks([])
pl.yticks([])
pl.imshow(v.reshape(image.shape), vmin=0, vmax=1)
pl.subplot(2, 3, 4)
pl.title('Objective Function')
pl.plot(algo.objectives)
pl.ylabel('objective')
pl.xlabel('iteration')
pl.subplot(2, 3, 5)
pl.title('Errors')
pl.plot(algo.errors)
pl.ylabel('error')
pl.xlabel('iteration')
pl.draw()
pl.show()
def main():
image = lena().astype(np.float) / 255.
h, w = image.shape
y_true = image.ravel()
noise = np.random.normal(0, 0.1, y_true.shape)
y_noisy = y_true + noise
grad = image_gradient_operator(h, w)
l1 = 0.1 * GroupL1Norm((2, h, w), 0)
#l1 = 0.1 * SliceSeparableNorm(L2Norm(), (2, h * w), 1)
l2 = L2Distance(y_noisy)
obj = lambda x: l1(grad * x) + l2(x)
algo = APGM(l2, l1, A=grad, maxiter=50, x0=y_noisy,
objectives=ObjectiveLogger(obj),
errors=ErrorLogger(y_true) )
t0 = time.time()
y_denoised = algo.run()
print "took %.3f seconds" % (time.time() - t0)
pl.figure()
pl.gray()
for i, (title, v) in enumerate([('ground truth', y_true),
('noisy', y_noisy),
('denoised', y_denoised)]):
pl.subplot(2, 3, i+1)
pl.title(title)
pl.xticks([])
pl.yticks([])
pl.imshow(v.reshape(image.shape), vmin=0, vmax=1)
pl.subplot(2, 3, 4)
pl.title('Objective Function')
pl.plot(algo.objectives)
pl.ylabel('objective')
pl.xlabel('iteration')
pl.subplot(2, 3, 5)
pl.title('Errors')
pl.plot(algo.errors)
pl.ylabel('error')
pl.xlabel('iteration')
pl.draw()
pl.show()
# measure b = A x
b = A.matvec(x)
# setup problem argmin_x 0.5 ||A x - b||_2^2 + ||x||_1
l1 = 1e-2 * L1Norm()
l2 = DataTerm(A, b)
# solve
maxiter = 5000
dr = DouglasRachford(l2, l1, gamma=0.1, maxiter=maxiter, objectives=ObjectiveLogger(l1 + l2), errors=ErrorLogger(x))
dr.run()
print "reasons for stopping: " + ", ".join(message for cls, message in dr.stopping_reasons)
np.testing.assert_array_almost_equal(x, dr.x, decimal=3)
apgm = APGM(l2, l1, rho=0.5, maxiter=maxiter, objectives=ObjectiveLogger(l1 + l2), errors=ErrorLogger(x))
apgm.run()
print "reasons for stopping: " + ", ".join(message for cls, message in apgm.stopping_reasons)
np.testing.assert_array_almost_equal(x, apgm.x, decimal=3)
alg1 = ForwardBackward(l1, l2, maxiter=maxiter, objectives=ObjectiveLogger(l1 + l2), errors=ErrorLogger(x))
alg1.run()
print "reasons for stopping: " + ", ".join(message for cls, message in alg1.stopping_reasons)
np.testing.assert_array_almost_equal(x, alg1.x, decimal=3)
xr = forward_backward(l1, l2, maxiter=maxiter)
np.testing.assert_array_equal(alg1.x, xr)
alg2 = ForwardBackward(l1, l2, maxiter=maxiter, alpha=0.9, objectives=ObjectiveLogger(l1 + l2), errors=ErrorLogger(x))
alg2.run()
print "reasons for stopping: " + ", ".join(message for cls, message in alg2.stopping_reasons)
